Abstract: The modification of jets in heavy-ion collisions, a phenomenon commonly called "jet quenching", is one of the main tools to determine the properties of the QCD matter created under these extreme conditions. In vacuum, jets are precisely described within perturbative QCD and can therefore serve as well-calibrated and highly versatile probes. Their description relies heavily on the phenomenon of color coherence, which introduces an ordering of subsequent emissions that reduces the complexity of these multi-particle processes. We will describe how the presence of a hot and dense background field alters the jet by decohering particles in the cascade and by inducing additional soft radiation. These effects are governed by one, common medium resolution scale, related to the dynamical transport properties of the plasma, which competes with the intrinsic jet scales in the course of the evolution. This scale allows us to rearrange the jet shower into effective charges that are sensitive to medium effects which, nevertheless, leave their internal structure unaffected. In particular, we explore the potential of measuring high-energy, collimated jets in Pb+Pb collisions at the LHC and show how to establish a jet calculus in medium.